As data communication networks become more and more pervasive, there is an increasing level of interest in optimizing network performance and improving network utilization in terms of throughput, end to end delay, packet loss, etc. For example, data communication networks may be analyzed and optimized for purposes of congestion handling, capacity estimation, and deep visualization of network performance, among others.
Network performance analysis and optimization requires an understanding of the actual traffic carried by the network, including the statistical properties of the network traffic. There are a number of mathematical models that can be used to model the statistical properties of real world network traffic. A common practice in network design is to create a simulation model of a network or device and subject the model to a traffic pattern created by the traffic models. The results from the simulation are used to fine-tune parameters of the device or network, such as queue length, buffer sizes, etc. However, as this approach involves modeling the network device and its characteristics, the analysis may suffer from simulation inaccuracies if assumptions made in generating the network model are incorrect.
Modern data communication networks are designed to carry a heterogeneous mix of traffic classes, including voice, video and data services. Thus, various mathematical models may be used in the analysis and testing of such systems.
There are a number of mathematical models for generating traffic that mimic real world traffic carried by a network. One of the basic traffic models is the Bernoulli source model, which generates packets at random intervals. A Bernoulli source is a non-correlated packet source. That is, new packets are generated based on probabilities that are independent of any previous event. The load offered by a Bernoulli traffic source is specified by ‘p’, probability of a packet arrival in a given time slot, which is independent of arrivals in previous time slots.
A second type of traffic source is an On-Off traffic source. The On-Off source operates as a two state Markov Chain. In the ON state, the source generates a packet with a defined level of probability. In the OFF state, no packets are generated. Two parameters are required for the On-Off traffic source: offered load, and average burst length.
Bernoulli source models and On-Off Discrete Markov Source Models will now be discussed in more detail.
Bernoulli Traffic Source Model
The Bernoulli traffic source generates packets according to a Bernoulli discrete random process. A single parameter, p (probability of arrival), is specified for the source. The offered load per input port is equal to the probability of arrival, p. Assume that the probability p of arrival is given as follows:Prob(1 arrival)=p  [1]while the probability of no arrival is given as:Prob(0 arrivals)=1−p  [2]
The Bernoulli source model is a memoryless process. That is, knowledge of a past arrival does not help predict a current or future arrival.
The Bernoulli distribution is only relevant when traffic intensity to an ingress port is less than 100%.
On-Off Discrete Markov Source Model
An On-Off Markov Modulated Process (MMP) is a bursty traffic source model of a discrete-time, 2-state (ON or OFF) Markov process. A MMP rapidly changes the injection process for bursty traffic. In an MMP source, the rate of a Bernoulli injection process is modulated by current state of Markov chain. A two state Markov chain is illustrated in FIG. 1.
As shown therein, a source can be modeled with two states, namely, “ON” and “OFF”. In the ON state, the source has an injection rate of r1; in the OFF state, the injection rate is 0. At each simulation loop, the probability of transitioning from the OFF state to the ON state is ‘a’, while the probability of transitioning from the ON state to the OFF state is ‘b’. Accordingly, the probability of staying in the OFF state (i.e., transitioning from the OFF state to the OFF state), while the probability of staying in the ON state (i.e., transitioning from the ON state to the ON state) is 1−b.
This two state MMP model represents a bursty injection process, in which during the bursts (i.e., in the ON state), injection occurs with an overall rate r1 with random inter packet delays, and outside the bursts (i.e. in the OFF state), the injection process is quiet.
Moreover, in this MMP model, the average length of a burst is given by 1/b and average time between bursts is 1/a (i.e. the “quiet time”). To determine the injection rate, a steady state distribution between the on and off states is assumed. The probability of being in the OFF state is x0, while the probability of being in the ON state is x1. Then in steady state:ax0=bx1  [3]wherex0+x1=1[4]
The steady state probability of being in the ON state is given as:x1=a/(a+b)  [5]
Therefore, the injection rate r of this MMP is given as:r=r1*x1=a*r1/(a+b)  [6]
From equation[6], it is clear that injection rate during the burst period is 1+(b/a) times the average injection rate. The larger the ratio of b to a, the more intense is the rate during the burst period. For example, for the following parameters                Average load: r=40%        b=0.01        a=0.005        
The ratio of b/a=0.01/0.005=2. So, at the offered rate of 40% of capacity, the MMP process alternates between periods of no packet injections and Bernoulli at a load of 40 (1+2)=120% of capacity. This level of burstiness may increase the average latency and/or reduce the saturation throughput of the device or system under consideration.
The On-Off model is a special case of Markov based traffic models in which there are at most 2 states. However, in general, a Markov-based traffic model may be represented as an n-state continuous time Markov process M={M(t)} t=0 to ∞, where the state space is {S1, S2, . . . , Sn}. That is, M(t)ε{S1, S2, . . . , Sn}.
Qualitatively, this means that the system can switch among any one of n different states, each of which may represent a different level of network traffic.
The process M stays in state Si for an exponentially distributed holding time, and then jumps to state Sj with probability Pij. More generally, all the state transitions (e.g. transitions from state S1 to S2, S5 to S4, S3 to Sn, etc.), are governed by a probability state matrix P≦[Pij], were Pij represent the probability of transition from state i to j.
Markov modulated traffic models constitute an important class of traffic models. In these models, the probability law of traffic arrivals in determined by the specific state in which the Markov process M is in. For example, while M is in state Sk, the probability law of traffic arrivals is completely determined by k, a property which holds for every value of k from 1 to n. When the Markov process M undergoes a transition to, for example, state Sj, then a new probability law takes effect for the duration of state Sj, and so on.
The most commonly used Markov-modulated model is a MMPP (Markov-Modulated Poisson process) model. In an MMPP, the modulation mechanism simply stipulates that in the state Sk of the process M, arrivals occur according to a Poisson process at rate λK. As the state changes, so does the rate.
Traffic Models and SLA Analytics.
Ensuring that performance requirements of data communication networks are met requires accurate verification and monitoring of Service Level Agreements (SLAs) to which the networks are subject. An SLA analytics tool set with rich features is almost a mandatory component of any IP vendor portfolio. Network SLA verification involves evaluation of a network's key performance indicators (e.g., bandwidth, jitter, latency, loss, etc.) under different traffic profiles (described by parameters, such as traffic type, rate, pattern etc). These traffic profiles are the result of traffic flows generated by applications at a higher level.
In statistical classification, traffic flows are identified based on their behavior. The ‘behavior’ of a traffic flow is quantified by observing packet arrivals for that flow belonging to a particular application type, and may discriminated from a known behavioral mode of an application type. The statistical characteristics of a traffic flow include mean inter-packet delay, packet size, arrival pattern etc. Mathematical traffic sources models can be used to generate traffic flows with these statistical parameters. Such sources can be used in the training phase of SLA analyzers.
FIG. 2 illustrates an architectural over view of a setup used for SLA analytics. As shown therein, a SLA analyzer 10 sends measurement configuration and setup information to a sender 20. Based on the configuration data provided by the SLA analyzer 10, the sender 20 sends measurement traffic through an IP network 30 to a receiver 40. The receiver prepares measurement reports and sends the measurement reports to the SLA analyzer 10.
Performance testing is largely done using a third party test equipment. These solutions are typically expensive and inflexible. Newer hardware and software modules need to be purchased for test cases covering emerging applications and scaling requirements.